Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6029,2,Mod(1,6029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6029 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1418073786\) |
Analytic rank: | \(1\) |
Dimension: | \(234\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6029.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45423 | −1.73540 | −0.867702 | − | 0.497084i | \(-0.834404\pi\) | ||||
−0.867702 | + | 0.497084i | \(0.834404\pi\) | |||||||
\(3\) | 2.05779 | 1.18807 | 0.594033 | − | 0.804441i | \(-0.297535\pi\) | ||||
0.594033 | + | 0.804441i | \(0.297535\pi\) | |||||||
\(4\) | 4.02326 | 2.01163 | ||||||||
\(5\) | −1.79809 | −0.804130 | −0.402065 | − | 0.915611i | \(-0.631707\pi\) | ||||
−0.402065 | + | 0.915611i | \(0.631707\pi\) | |||||||
\(6\) | −5.05030 | −2.06177 | ||||||||
\(7\) | 3.33599 | 1.26088 | 0.630442 | − | 0.776236i | \(-0.282873\pi\) | ||||
0.630442 | + | 0.776236i | \(0.282873\pi\) | |||||||
\(8\) | −4.96555 | −1.75559 | ||||||||
\(9\) | 1.23450 | 0.411500 | ||||||||
\(10\) | 4.41293 | 1.39549 | ||||||||
\(11\) | 2.39546 | 0.722258 | 0.361129 | − | 0.932516i | \(-0.382391\pi\) | ||||
0.361129 | + | 0.932516i | \(0.382391\pi\) | |||||||
\(12\) | 8.27902 | 2.38995 | ||||||||
\(13\) | −6.12503 | −1.69878 | −0.849389 | − | 0.527768i | \(-0.823029\pi\) | ||||
−0.849389 | + | 0.527768i | \(0.823029\pi\) | |||||||
\(14\) | −8.18729 | −2.18815 | ||||||||
\(15\) | −3.70009 | −0.955360 | ||||||||
\(16\) | 4.14010 | 1.03502 | ||||||||
\(17\) | −4.09021 | −0.992021 | −0.496010 | − | 0.868317i | \(-0.665202\pi\) | ||||
−0.496010 | + | 0.868317i | \(0.665202\pi\) | |||||||
\(18\) | −3.02975 | −0.714118 | ||||||||
\(19\) | 1.64645 | 0.377722 | 0.188861 | − | 0.982004i | \(-0.439520\pi\) | ||||
0.188861 | + | 0.982004i | \(0.439520\pi\) | |||||||
\(20\) | −7.23418 | −1.61761 | ||||||||
\(21\) | 6.86476 | 1.49801 | ||||||||
\(22\) | −5.87901 | −1.25341 | ||||||||
\(23\) | −1.16024 | −0.241926 | −0.120963 | − | 0.992657i | \(-0.538598\pi\) | ||||
−0.120963 | + | 0.992657i | \(0.538598\pi\) | |||||||
\(24\) | −10.2181 | −2.08575 | ||||||||
\(25\) | −1.76687 | −0.353374 | ||||||||
\(26\) | 15.0323 | 2.94807 | ||||||||
\(27\) | −3.63303 | −0.699177 | ||||||||
\(28\) | 13.4215 | 2.53643 | ||||||||
\(29\) | 8.83975 | 1.64150 | 0.820750 | − | 0.571287i | \(-0.193556\pi\) | ||||
0.820750 | + | 0.571287i | \(0.193556\pi\) | |||||||
\(30\) | 9.08089 | 1.65794 | ||||||||
\(31\) | −9.45409 | −1.69801 | −0.849003 | − | 0.528389i | \(-0.822796\pi\) | ||||
−0.849003 | + | 0.528389i | \(0.822796\pi\) | |||||||
\(32\) | −0.229666 | −0.0405997 | ||||||||
\(33\) | 4.92935 | 0.858090 | ||||||||
\(34\) | 10.0383 | 1.72156 | ||||||||
\(35\) | −5.99841 | −1.01392 | ||||||||
\(36\) | 4.96671 | 0.827785 | ||||||||
\(37\) | −0.0716628 | −0.0117813 | −0.00589065 | − | 0.999983i | \(-0.501875\pi\) | ||||
−0.00589065 | + | 0.999983i | \(0.501875\pi\) | |||||||
\(38\) | −4.04078 | −0.655501 | ||||||||
\(39\) | −12.6040 | −2.01826 | ||||||||
\(40\) | 8.92851 | 1.41172 | ||||||||
\(41\) | 6.84880 | 1.06960 | 0.534801 | − | 0.844978i | \(-0.320386\pi\) | ||||
0.534801 | + | 0.844978i | \(0.320386\pi\) | |||||||
\(42\) | −16.8477 | −2.59966 | ||||||||
\(43\) | 7.58637 | 1.15691 | 0.578455 | − | 0.815714i | \(-0.303656\pi\) | ||||
0.578455 | + | 0.815714i | \(0.303656\pi\) | |||||||
\(44\) | 9.63755 | 1.45292 | ||||||||
\(45\) | −2.21974 | −0.330899 | ||||||||
\(46\) | 2.84749 | 0.419839 | ||||||||
\(47\) | 5.93310 | 0.865431 | 0.432716 | − | 0.901530i | \(-0.357555\pi\) | ||||
0.432716 | + | 0.901530i | \(0.357555\pi\) | |||||||
\(48\) | 8.51945 | 1.22968 | ||||||||
\(49\) | 4.12882 | 0.589831 | ||||||||
\(50\) | 4.33632 | 0.613248 | ||||||||
\(51\) | −8.41678 | −1.17859 | ||||||||
\(52\) | −24.6426 | −3.41731 | ||||||||
\(53\) | 5.04954 | 0.693608 | 0.346804 | − | 0.937938i | \(-0.387267\pi\) | ||||
0.346804 | + | 0.937938i | \(0.387267\pi\) | |||||||
\(54\) | 8.91630 | 1.21336 | ||||||||
\(55\) | −4.30725 | −0.580790 | ||||||||
\(56\) | −16.5650 | −2.21359 | ||||||||
\(57\) | 3.38805 | 0.448759 | ||||||||
\(58\) | −21.6948 | −2.84867 | ||||||||
\(59\) | 5.49282 | 0.715104 | 0.357552 | − | 0.933893i | \(-0.383612\pi\) | ||||
0.357552 | + | 0.933893i | \(0.383612\pi\) | |||||||
\(60\) | −14.8864 | −1.92183 | ||||||||
\(61\) | 3.13441 | 0.401321 | 0.200660 | − | 0.979661i | \(-0.435691\pi\) | ||||
0.200660 | + | 0.979661i | \(0.435691\pi\) | |||||||
\(62\) | 23.2025 | 2.94673 | ||||||||
\(63\) | 4.11827 | 0.518854 | ||||||||
\(64\) | −7.71654 | −0.964568 | ||||||||
\(65\) | 11.0134 | 1.36604 | ||||||||
\(66\) | −12.0978 | −1.48913 | ||||||||
\(67\) | 2.64537 | 0.323184 | 0.161592 | − | 0.986858i | \(-0.448337\pi\) | ||||
0.161592 | + | 0.986858i | \(0.448337\pi\) | |||||||
\(68\) | −16.4560 | −1.99558 | ||||||||
\(69\) | −2.38752 | −0.287424 | ||||||||
\(70\) | 14.7215 | 1.75955 | ||||||||
\(71\) | −6.30184 | −0.747891 | −0.373945 | − | 0.927451i | \(-0.621995\pi\) | ||||
−0.373945 | + | 0.927451i | \(0.621995\pi\) | |||||||
\(72\) | −6.12997 | −0.722424 | ||||||||
\(73\) | −7.88700 | −0.923103 | −0.461552 | − | 0.887113i | \(-0.652707\pi\) | ||||
−0.461552 | + | 0.887113i | \(0.652707\pi\) | |||||||
\(74\) | 0.175877 | 0.0204453 | ||||||||
\(75\) | −3.63585 | −0.419832 | ||||||||
\(76\) | 6.62411 | 0.759837 | ||||||||
\(77\) | 7.99122 | 0.910684 | ||||||||
\(78\) | 30.9332 | 3.50250 | ||||||||
\(79\) | −12.1333 | −1.36510 | −0.682551 | − | 0.730838i | \(-0.739130\pi\) | ||||
−0.682551 | + | 0.730838i | \(0.739130\pi\) | |||||||
\(80\) | −7.44427 | −0.832295 | ||||||||
\(81\) | −11.1795 | −1.24217 | ||||||||
\(82\) | −16.8085 | −1.85619 | ||||||||
\(83\) | −11.0120 | −1.20872 | −0.604362 | − | 0.796709i | \(-0.706572\pi\) | ||||
−0.604362 | + | 0.796709i | \(0.706572\pi\) | |||||||
\(84\) | 27.6187 | 3.01345 | ||||||||
\(85\) | 7.35456 | 0.797714 | ||||||||
\(86\) | −18.6187 | −2.00771 | ||||||||
\(87\) | 18.1904 | 1.95021 | ||||||||
\(88\) | −11.8948 | −1.26799 | ||||||||
\(89\) | −7.98323 | −0.846221 | −0.423111 | − | 0.906078i | \(-0.639062\pi\) | ||||
−0.423111 | + | 0.906078i | \(0.639062\pi\) | |||||||
\(90\) | 5.44776 | 0.574244 | ||||||||
\(91\) | −20.4330 | −2.14196 | ||||||||
\(92\) | −4.66793 | −0.486665 | ||||||||
\(93\) | −19.4545 | −2.01734 | ||||||||
\(94\) | −14.5612 | −1.50187 | ||||||||
\(95\) | −2.96047 | −0.303738 | ||||||||
\(96\) | −0.472605 | −0.0482351 | ||||||||
\(97\) | −17.2257 | −1.74900 | −0.874501 | − | 0.485024i | \(-0.838811\pi\) | ||||
−0.874501 | + | 0.485024i | \(0.838811\pi\) | |||||||
\(98\) | −10.1331 | −1.02360 | ||||||||
\(99\) | 2.95719 | 0.297209 | ||||||||
\(100\) | −7.10858 | −0.710858 | ||||||||
\(101\) | 6.33659 | 0.630514 | 0.315257 | − | 0.949006i | \(-0.397909\pi\) | ||||
0.315257 | + | 0.949006i | \(0.397909\pi\) | |||||||
\(102\) | 20.6567 | 2.04532 | ||||||||
\(103\) | −4.14282 | −0.408204 | −0.204102 | − | 0.978950i | \(-0.565427\pi\) | ||||
−0.204102 | + | 0.978950i | \(0.565427\pi\) | |||||||
\(104\) | 30.4141 | 2.98235 | ||||||||
\(105\) | −12.3435 | −1.20460 | ||||||||
\(106\) | −12.3928 | −1.20369 | ||||||||
\(107\) | 7.49093 | 0.724175 | 0.362088 | − | 0.932144i | \(-0.382064\pi\) | ||||
0.362088 | + | 0.932144i | \(0.382064\pi\) | |||||||
\(108\) | −14.6166 | −1.40649 | ||||||||
\(109\) | −4.90706 | −0.470011 | −0.235006 | − | 0.971994i | \(-0.575511\pi\) | ||||
−0.235006 | + | 0.971994i | \(0.575511\pi\) | |||||||
\(110\) | 10.5710 | 1.00791 | ||||||||
\(111\) | −0.147467 | −0.0139969 | ||||||||
\(112\) | 13.8113 | 1.30505 | ||||||||
\(113\) | 14.9221 | 1.40375 | 0.701876 | − | 0.712300i | \(-0.252346\pi\) | ||||
0.701876 | + | 0.712300i | \(0.252346\pi\) | |||||||
\(114\) | −8.31507 | −0.778778 | ||||||||
\(115\) | 2.08621 | 0.194540 | ||||||||
\(116\) | 35.5646 | 3.30209 | ||||||||
\(117\) | −7.56134 | −0.699046 | ||||||||
\(118\) | −13.4806 | −1.24099 | ||||||||
\(119\) | −13.6449 | −1.25082 | ||||||||
\(120\) | 18.3730 | 1.67722 | ||||||||
\(121\) | −5.26178 | −0.478343 | ||||||||
\(122\) | −7.69258 | −0.696454 | ||||||||
\(123\) | 14.0934 | 1.27076 | ||||||||
\(124\) | −38.0363 | −3.41576 | ||||||||
\(125\) | 12.1674 | 1.08829 | ||||||||
\(126\) | −10.1072 | −0.900421 | ||||||||
\(127\) | 13.6509 | 1.21132 | 0.605659 | − | 0.795724i | \(-0.292909\pi\) | ||||
0.605659 | + | 0.795724i | \(0.292909\pi\) | |||||||
\(128\) | 19.3975 | 1.71452 | ||||||||
\(129\) | 15.6112 | 1.37449 | ||||||||
\(130\) | −27.0293 | −2.37063 | ||||||||
\(131\) | −13.6674 | −1.19412 | −0.597061 | − | 0.802196i | \(-0.703665\pi\) | ||||
−0.597061 | + | 0.802196i | \(0.703665\pi\) | |||||||
\(132\) | 19.8321 | 1.72616 | ||||||||
\(133\) | 5.49255 | 0.476264 | ||||||||
\(134\) | −6.49237 | −0.560855 | ||||||||
\(135\) | 6.53252 | 0.562229 | ||||||||
\(136\) | 20.3101 | 1.74158 | ||||||||
\(137\) | −9.99634 | −0.854045 | −0.427022 | − | 0.904241i | \(-0.640437\pi\) | ||||
−0.427022 | + | 0.904241i | \(0.640437\pi\) | |||||||
\(138\) | 5.85953 | 0.498797 | ||||||||
\(139\) | −18.1146 | −1.53646 | −0.768232 | − | 0.640171i | \(-0.778863\pi\) | ||||
−0.768232 | + | 0.640171i | \(0.778863\pi\) | |||||||
\(140\) | −24.1332 | −2.03962 | ||||||||
\(141\) | 12.2091 | 1.02819 | ||||||||
\(142\) | 15.4662 | 1.29789 | ||||||||
\(143\) | −14.6723 | −1.22696 | ||||||||
\(144\) | 5.11095 | 0.425912 | ||||||||
\(145\) | −15.8947 | −1.31998 | ||||||||
\(146\) | 19.3565 | 1.60196 | ||||||||
\(147\) | 8.49624 | 0.700758 | ||||||||
\(148\) | −0.288318 | −0.0236996 | ||||||||
\(149\) | 5.29357 | 0.433666 | 0.216833 | − | 0.976209i | \(-0.430427\pi\) | ||||
0.216833 | + | 0.976209i | \(0.430427\pi\) | |||||||
\(150\) | 8.92323 | 0.728578 | ||||||||
\(151\) | −21.0927 | −1.71650 | −0.858249 | − | 0.513234i | \(-0.828447\pi\) | ||||
−0.858249 | + | 0.513234i | \(0.828447\pi\) | |||||||
\(152\) | −8.17554 | −0.663124 | ||||||||
\(153\) | −5.04935 | −0.408216 | ||||||||
\(154\) | −19.6123 | −1.58041 | ||||||||
\(155\) | 16.9993 | 1.36542 | ||||||||
\(156\) | −50.7093 | −4.05999 | ||||||||
\(157\) | 5.60951 | 0.447688 | 0.223844 | − | 0.974625i | \(-0.428139\pi\) | ||||
0.223844 | + | 0.974625i | \(0.428139\pi\) | |||||||
\(158\) | 29.7779 | 2.36901 | ||||||||
\(159\) | 10.3909 | 0.824052 | ||||||||
\(160\) | 0.412961 | 0.0326474 | ||||||||
\(161\) | −3.87053 | −0.305041 | ||||||||
\(162\) | 27.4371 | 2.15566 | ||||||||
\(163\) | 14.5856 | 1.14243 | 0.571216 | − | 0.820800i | \(-0.306472\pi\) | ||||
0.571216 | + | 0.820800i | \(0.306472\pi\) | |||||||
\(164\) | 27.5545 | 2.15164 | ||||||||
\(165\) | −8.86342 | −0.690016 | ||||||||
\(166\) | 27.0260 | 2.09763 | ||||||||
\(167\) | −22.0799 | −1.70859 | −0.854295 | − | 0.519788i | \(-0.826011\pi\) | ||||
−0.854295 | + | 0.519788i | \(0.826011\pi\) | |||||||
\(168\) | −34.0873 | −2.62989 | ||||||||
\(169\) | 24.5160 | 1.88585 | ||||||||
\(170\) | −18.0498 | −1.38436 | ||||||||
\(171\) | 2.03254 | 0.155433 | ||||||||
\(172\) | 30.5219 | 2.32728 | ||||||||
\(173\) | −21.2826 | −1.61809 | −0.809043 | − | 0.587749i | \(-0.800014\pi\) | ||||
−0.809043 | + | 0.587749i | \(0.800014\pi\) | |||||||
\(174\) | −44.6434 | −3.38440 | ||||||||
\(175\) | −5.89426 | −0.445564 | ||||||||
\(176\) | 9.91744 | 0.747555 | ||||||||
\(177\) | 11.3031 | 0.849590 | ||||||||
\(178\) | 19.5927 | 1.46854 | ||||||||
\(179\) | −21.8814 | −1.63549 | −0.817746 | − | 0.575580i | \(-0.804776\pi\) | ||||
−0.817746 | + | 0.575580i | \(0.804776\pi\) | |||||||
\(180\) | −8.93059 | −0.665647 | ||||||||
\(181\) | −1.02528 | −0.0762087 | −0.0381043 | − | 0.999274i | \(-0.512132\pi\) | ||||
−0.0381043 | + | 0.999274i | \(0.512132\pi\) | |||||||
\(182\) | 50.1474 | 3.71717 | ||||||||
\(183\) | 6.44996 | 0.476795 | ||||||||
\(184\) | 5.76121 | 0.424722 | ||||||||
\(185\) | 0.128856 | 0.00947369 | ||||||||
\(186\) | 47.7460 | 3.50090 | ||||||||
\(187\) | −9.79792 | −0.716495 | ||||||||
\(188\) | 23.8704 | 1.74093 | ||||||||
\(189\) | −12.1197 | −0.881582 | ||||||||
\(190\) | 7.26568 | 0.527108 | ||||||||
\(191\) | −19.4767 | −1.40929 | −0.704643 | − | 0.709562i | \(-0.748893\pi\) | ||||
−0.704643 | + | 0.709562i | \(0.748893\pi\) | |||||||
\(192\) | −15.8790 | −1.14597 | ||||||||
\(193\) | 8.33075 | 0.599660 | 0.299830 | − | 0.953993i | \(-0.403070\pi\) | ||||
0.299830 | + | 0.953993i | \(0.403070\pi\) | |||||||
\(194\) | 42.2758 | 3.03523 | ||||||||
\(195\) | 22.6632 | 1.62294 | ||||||||
\(196\) | 16.6113 | 1.18652 | ||||||||
\(197\) | 10.7810 | 0.768117 | 0.384059 | − | 0.923309i | \(-0.374526\pi\) | ||||
0.384059 | + | 0.923309i | \(0.374526\pi\) | |||||||
\(198\) | −7.25764 | −0.515778 | ||||||||
\(199\) | −10.0163 | −0.710036 | −0.355018 | − | 0.934859i | \(-0.615525\pi\) | ||||
−0.355018 | + | 0.934859i | \(0.615525\pi\) | |||||||
\(200\) | 8.77349 | 0.620380 | ||||||||
\(201\) | 5.44362 | 0.383964 | ||||||||
\(202\) | −15.5515 | −1.09420 | ||||||||
\(203\) | 29.4893 | 2.06974 | ||||||||
\(204\) | −33.8629 | −2.37088 | ||||||||
\(205\) | −12.3148 | −0.860100 | ||||||||
\(206\) | 10.1674 | 0.708400 | ||||||||
\(207\) | −1.43231 | −0.0995524 | ||||||||
\(208\) | −25.3582 | −1.75828 | ||||||||
\(209\) | 3.94401 | 0.272813 | ||||||||
\(210\) | 30.2937 | 2.09047 | ||||||||
\(211\) | 1.72654 | 0.118860 | 0.0594300 | − | 0.998232i | \(-0.481072\pi\) | ||||
0.0594300 | + | 0.998232i | \(0.481072\pi\) | |||||||
\(212\) | 20.3156 | 1.39528 | ||||||||
\(213\) | −12.9679 | −0.888543 | ||||||||
\(214\) | −18.3845 | −1.25674 | ||||||||
\(215\) | −13.6410 | −0.930307 | ||||||||
\(216\) | 18.0400 | 1.22747 | ||||||||
\(217\) | −31.5387 | −2.14099 | ||||||||
\(218\) | 12.0431 | 0.815660 | ||||||||
\(219\) | −16.2298 | −1.09671 | ||||||||
\(220\) | −17.3292 | −1.16833 | ||||||||
\(221\) | 25.0526 | 1.68522 | ||||||||
\(222\) | 0.361918 | 0.0242904 | ||||||||
\(223\) | −11.2786 | −0.755274 | −0.377637 | − | 0.925954i | \(-0.623263\pi\) | ||||
−0.377637 | + | 0.925954i | \(0.623263\pi\) | |||||||
\(224\) | −0.766165 | −0.0511915 | ||||||||
\(225\) | −2.18120 | −0.145413 | ||||||||
\(226\) | −36.6223 | −2.43608 | ||||||||
\(227\) | −17.1229 | −1.13649 | −0.568245 | − | 0.822859i | \(-0.692377\pi\) | ||||
−0.568245 | + | 0.822859i | \(0.692377\pi\) | |||||||
\(228\) | 13.6310 | 0.902736 | ||||||||
\(229\) | −7.02069 | −0.463940 | −0.231970 | − | 0.972723i | \(-0.574517\pi\) | ||||
−0.231970 | + | 0.972723i | \(0.574517\pi\) | |||||||
\(230\) | −5.12004 | −0.337606 | ||||||||
\(231\) | 16.4443 | 1.08195 | ||||||||
\(232\) | −43.8942 | −2.88180 | ||||||||
\(233\) | 25.2366 | 1.65331 | 0.826654 | − | 0.562711i | \(-0.190242\pi\) | ||||
0.826654 | + | 0.562711i | \(0.190242\pi\) | |||||||
\(234\) | 18.5573 | 1.21313 | ||||||||
\(235\) | −10.6682 | −0.695920 | ||||||||
\(236\) | 22.0990 | 1.43852 | ||||||||
\(237\) | −24.9678 | −1.62183 | ||||||||
\(238\) | 33.4877 | 2.17069 | ||||||||
\(239\) | 16.1821 | 1.04673 | 0.523366 | − | 0.852108i | \(-0.324676\pi\) | ||||
0.523366 | + | 0.852108i | \(0.324676\pi\) | |||||||
\(240\) | −15.3187 | −0.988821 | ||||||||
\(241\) | −20.4815 | −1.31933 | −0.659664 | − | 0.751561i | \(-0.729301\pi\) | ||||
−0.659664 | + | 0.751561i | \(0.729301\pi\) | |||||||
\(242\) | 12.9136 | 0.830119 | ||||||||
\(243\) | −12.1060 | −0.776600 | ||||||||
\(244\) | 12.6106 | 0.807308 | ||||||||
\(245\) | −7.42398 | −0.474301 | ||||||||
\(246\) | −34.5885 | −2.20528 | ||||||||
\(247\) | −10.0846 | −0.641666 | ||||||||
\(248\) | 46.9448 | 2.98100 | ||||||||
\(249\) | −22.6604 | −1.43604 | ||||||||
\(250\) | −29.8617 | −1.88862 | ||||||||
\(251\) | −21.7112 | −1.37040 | −0.685200 | − | 0.728355i | \(-0.740285\pi\) | ||||
−0.685200 | + | 0.728355i | \(0.740285\pi\) | |||||||
\(252\) | 16.5689 | 1.04374 | ||||||||
\(253\) | −2.77930 | −0.174733 | ||||||||
\(254\) | −33.5024 | −2.10213 | ||||||||
\(255\) | 15.1341 | 0.947736 | ||||||||
\(256\) | −32.1730 | −2.01081 | ||||||||
\(257\) | −30.5269 | −1.90421 | −0.952107 | − | 0.305764i | \(-0.901088\pi\) | ||||
−0.952107 | + | 0.305764i | \(0.901088\pi\) | |||||||
\(258\) | −38.3134 | −2.38529 | ||||||||
\(259\) | −0.239066 | −0.0148549 | ||||||||
\(260\) | 44.3096 | 2.74796 | ||||||||
\(261\) | 10.9127 | 0.675477 | ||||||||
\(262\) | 33.5429 | 2.07229 | ||||||||
\(263\) | 12.2414 | 0.754836 | 0.377418 | − | 0.926043i | \(-0.376812\pi\) | ||||
0.377418 | + | 0.926043i | \(0.376812\pi\) | |||||||
\(264\) | −24.4769 | −1.50645 | ||||||||
\(265\) | −9.07953 | −0.557751 | ||||||||
\(266\) | −13.4800 | −0.826511 | ||||||||
\(267\) | −16.4278 | −1.00537 | ||||||||
\(268\) | 10.6430 | 0.650126 | ||||||||
\(269\) | −5.18245 | −0.315979 | −0.157990 | − | 0.987441i | \(-0.550501\pi\) | ||||
−0.157990 | + | 0.987441i | \(0.550501\pi\) | |||||||
\(270\) | −16.0323 | −0.975696 | ||||||||
\(271\) | 7.40101 | 0.449579 | 0.224790 | − | 0.974407i | \(-0.427831\pi\) | ||||
0.224790 | + | 0.974407i | \(0.427831\pi\) | |||||||
\(272\) | −16.9339 | −1.02677 | ||||||||
\(273\) | −42.0469 | −2.54479 | ||||||||
\(274\) | 24.5333 | 1.48211 | ||||||||
\(275\) | −4.23247 | −0.255227 | ||||||||
\(276\) | −9.60562 | −0.578190 | ||||||||
\(277\) | 9.22650 | 0.554367 | 0.277183 | − | 0.960817i | \(-0.410599\pi\) | ||||
0.277183 | + | 0.960817i | \(0.410599\pi\) | |||||||
\(278\) | 44.4576 | 2.66639 | ||||||||
\(279\) | −11.6711 | −0.698729 | ||||||||
\(280\) | 29.7854 | 1.78002 | ||||||||
\(281\) | −13.2871 | −0.792643 | −0.396322 | − | 0.918112i | \(-0.629714\pi\) | ||||
−0.396322 | + | 0.918112i | \(0.629714\pi\) | |||||||
\(282\) | −29.9639 | −1.78432 | ||||||||
\(283\) | 21.8447 | 1.29853 | 0.649266 | − | 0.760562i | \(-0.275076\pi\) | ||||
0.649266 | + | 0.760562i | \(0.275076\pi\) | |||||||
\(284\) | −25.3539 | −1.50448 | ||||||||
\(285\) | −6.09203 | −0.360860 | ||||||||
\(286\) | 36.0091 | 2.12927 | ||||||||
\(287\) | 22.8475 | 1.34865 | ||||||||
\(288\) | −0.283523 | −0.0167068 | ||||||||
\(289\) | −0.270221 | −0.0158953 | ||||||||
\(290\) | 39.0092 | 2.29070 | ||||||||
\(291\) | −35.4468 | −2.07793 | ||||||||
\(292\) | −31.7314 | −1.85694 | ||||||||
\(293\) | 12.6445 | 0.738700 | 0.369350 | − | 0.929290i | \(-0.379580\pi\) | ||||
0.369350 | + | 0.929290i | \(0.379580\pi\) | |||||||
\(294\) | −20.8517 | −1.21610 | ||||||||
\(295\) | −9.87658 | −0.575037 | ||||||||
\(296\) | 0.355845 | 0.0206831 | ||||||||
\(297\) | −8.70277 | −0.504986 | ||||||||
\(298\) | −12.9917 | −0.752587 | ||||||||
\(299\) | 7.10648 | 0.410978 | ||||||||
\(300\) | −14.6280 | −0.844546 | ||||||||
\(301\) | 25.3080 | 1.45873 | ||||||||
\(302\) | 51.7663 | 2.97882 | ||||||||
\(303\) | 13.0394 | 0.749092 | ||||||||
\(304\) | 6.81648 | 0.390952 | ||||||||
\(305\) | −5.63596 | −0.322714 | ||||||||
\(306\) | 12.3923 | 0.708420 | ||||||||
\(307\) | −16.1229 | −0.920184 | −0.460092 | − | 0.887871i | \(-0.652184\pi\) | ||||
−0.460092 | + | 0.887871i | \(0.652184\pi\) | |||||||
\(308\) | 32.1508 | 1.83196 | ||||||||
\(309\) | −8.52505 | −0.484973 | ||||||||
\(310\) | −41.7203 | −2.36955 | ||||||||
\(311\) | −10.0487 | −0.569810 | −0.284905 | − | 0.958556i | \(-0.591962\pi\) | ||||
−0.284905 | + | 0.958556i | \(0.591962\pi\) | |||||||
\(312\) | 62.5859 | 3.54323 | ||||||||
\(313\) | −27.0102 | −1.52671 | −0.763353 | − | 0.645982i | \(-0.776448\pi\) | ||||
−0.763353 | + | 0.645982i | \(0.776448\pi\) | |||||||
\(314\) | −13.7671 | −0.776920 | ||||||||
\(315\) | −7.40503 | −0.417226 | ||||||||
\(316\) | −48.8154 | −2.74608 | ||||||||
\(317\) | −4.47449 | −0.251312 | −0.125656 | − | 0.992074i | \(-0.540104\pi\) | ||||
−0.125656 | + | 0.992074i | \(0.540104\pi\) | |||||||
\(318\) | −25.5017 | −1.43006 | ||||||||
\(319\) | 21.1753 | 1.18559 | ||||||||
\(320\) | 13.8750 | 0.775638 | ||||||||
\(321\) | 15.4148 | 0.860368 | ||||||||
\(322\) | 9.49919 | 0.529369 | ||||||||
\(323\) | −6.73433 | −0.374708 | ||||||||
\(324\) | −44.9781 | −2.49878 | ||||||||
\(325\) | 10.8221 | 0.600304 | ||||||||
\(326\) | −35.7964 | −1.98258 | ||||||||
\(327\) | −10.0977 | −0.558404 | ||||||||
\(328\) | −34.0081 | −1.87778 | ||||||||
\(329\) | 19.7927 | 1.09121 | ||||||||
\(330\) | 21.7529 | 1.19746 | ||||||||
\(331\) | 7.29370 | 0.400898 | 0.200449 | − | 0.979704i | \(-0.435760\pi\) | ||||
0.200449 | + | 0.979704i | \(0.435760\pi\) | |||||||
\(332\) | −44.3042 | −2.43151 | ||||||||
\(333\) | −0.0884676 | −0.00484800 | ||||||||
\(334\) | 54.1891 | 2.96510 | ||||||||
\(335\) | −4.75662 | −0.259882 | ||||||||
\(336\) | 28.4208 | 1.55048 | ||||||||
\(337\) | 11.3404 | 0.617749 | 0.308875 | − | 0.951103i | \(-0.400048\pi\) | ||||
0.308875 | + | 0.951103i | \(0.400048\pi\) | |||||||
\(338\) | −60.1680 | −3.27271 | ||||||||
\(339\) | 30.7065 | 1.66775 | ||||||||
\(340\) | 29.5893 | 1.60470 | ||||||||
\(341\) | −22.6469 | −1.22640 | ||||||||
\(342\) | −4.98834 | −0.269738 | ||||||||
\(343\) | −9.57823 | −0.517176 | ||||||||
\(344\) | −37.6705 | −2.03106 | ||||||||
\(345\) | 4.29298 | 0.231126 | ||||||||
\(346\) | 52.2325 | 2.80804 | ||||||||
\(347\) | −4.25810 | −0.228587 | −0.114293 | − | 0.993447i | \(-0.536460\pi\) | ||||
−0.114293 | + | 0.993447i | \(0.536460\pi\) | |||||||
\(348\) | 73.1845 | 3.92310 | ||||||||
\(349\) | −14.2385 | −0.762169 | −0.381085 | − | 0.924540i | \(-0.624449\pi\) | ||||
−0.381085 | + | 0.924540i | \(0.624449\pi\) | |||||||
\(350\) | 14.4659 | 0.773235 | ||||||||
\(351\) | 22.2524 | 1.18775 | ||||||||
\(352\) | −0.550157 | −0.0293234 | ||||||||
\(353\) | 32.1199 | 1.70957 | 0.854785 | − | 0.518982i | \(-0.173689\pi\) | ||||
0.854785 | + | 0.518982i | \(0.173689\pi\) | |||||||
\(354\) | −27.7403 | −1.47438 | ||||||||
\(355\) | 11.3313 | 0.601402 | ||||||||
\(356\) | −32.1186 | −1.70228 | ||||||||
\(357\) | −28.0783 | −1.48606 | ||||||||
\(358\) | 53.7020 | 2.83824 | ||||||||
\(359\) | −9.57670 | −0.505439 | −0.252719 | − | 0.967540i | \(-0.581325\pi\) | ||||
−0.252719 | + | 0.967540i | \(0.581325\pi\) | |||||||
\(360\) | 11.0222 | 0.580923 | ||||||||
\(361\) | −16.2892 | −0.857326 | ||||||||
\(362\) | 2.51628 | 0.132253 | ||||||||
\(363\) | −10.8276 | −0.568303 | ||||||||
\(364\) | −82.2074 | −4.30884 | ||||||||
\(365\) | 14.1815 | 0.742295 | ||||||||
\(366\) | −15.8297 | −0.827432 | ||||||||
\(367\) | 2.18672 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(368\) | −4.80349 | −0.250399 | ||||||||
\(369\) | 8.45483 | 0.440141 | ||||||||
\(370\) | −0.316243 | −0.0164407 | ||||||||
\(371\) | 16.8452 | 0.874560 | ||||||||
\(372\) | −78.2707 | −4.05814 | ||||||||
\(373\) | 13.1840 | 0.682640 | 0.341320 | − | 0.939947i | \(-0.389126\pi\) | ||||
0.341320 | + | 0.939947i | \(0.389126\pi\) | |||||||
\(374\) | 24.0464 | 1.24341 | ||||||||
\(375\) | 25.0380 | 1.29296 | ||||||||
\(376\) | −29.4611 | −1.51934 | ||||||||
\(377\) | −54.1437 | −2.78854 | ||||||||
\(378\) | 29.7447 | 1.52990 | ||||||||
\(379\) | −2.79393 | −0.143515 | −0.0717573 | − | 0.997422i | \(-0.522861\pi\) | ||||
−0.0717573 | + | 0.997422i | \(0.522861\pi\) | |||||||
\(380\) | −11.9107 | −0.611008 | ||||||||
\(381\) | 28.0906 | 1.43913 | ||||||||
\(382\) | 47.8004 | 2.44568 | ||||||||
\(383\) | −15.3207 | −0.782853 | −0.391426 | − | 0.920209i | \(-0.628018\pi\) | ||||
−0.391426 | + | 0.920209i | \(0.628018\pi\) | |||||||
\(384\) | 39.9160 | 2.03696 | ||||||||
\(385\) | −14.3689 | −0.732309 | ||||||||
\(386\) | −20.4456 | −1.04065 | ||||||||
\(387\) | 9.36536 | 0.476068 | ||||||||
\(388\) | −69.3033 | −3.51834 | ||||||||
\(389\) | 6.20522 | 0.314617 | 0.157309 | − | 0.987550i | \(-0.449718\pi\) | ||||
0.157309 | + | 0.987550i | \(0.449718\pi\) | |||||||
\(390\) | −55.6207 | −2.81646 | ||||||||
\(391\) | 4.74560 | 0.239995 | ||||||||
\(392\) | −20.5018 | −1.03550 | ||||||||
\(393\) | −28.1245 | −1.41870 | ||||||||
\(394\) | −26.4592 | −1.33299 | ||||||||
\(395\) | 21.8168 | 1.09772 | ||||||||
\(396\) | 11.8975 | 0.597874 | ||||||||
\(397\) | 15.3064 | 0.768206 | 0.384103 | − | 0.923290i | \(-0.374511\pi\) | ||||
0.384103 | + | 0.923290i | \(0.374511\pi\) | |||||||
\(398\) | 24.5823 | 1.23220 | ||||||||
\(399\) | 11.3025 | 0.565833 | ||||||||
\(400\) | −7.31502 | −0.365751 | ||||||||
\(401\) | 18.6056 | 0.929120 | 0.464560 | − | 0.885542i | \(-0.346212\pi\) | ||||
0.464560 | + | 0.885542i | \(0.346212\pi\) | |||||||
\(402\) | −13.3599 | −0.666332 | ||||||||
\(403\) | 57.9066 | 2.88453 | ||||||||
\(404\) | 25.4938 | 1.26836 | ||||||||
\(405\) | 20.1018 | 0.998865 | ||||||||
\(406\) | −72.3736 | −3.59184 | ||||||||
\(407\) | −0.171665 | −0.00850913 | ||||||||
\(408\) | 41.7940 | 2.06911 | ||||||||
\(409\) | 28.3336 | 1.40101 | 0.700503 | − | 0.713649i | \(-0.252959\pi\) | ||||
0.700503 | + | 0.713649i | \(0.252959\pi\) | |||||||
\(410\) | 30.2233 | 1.49262 | ||||||||
\(411\) | −20.5704 | −1.01466 | ||||||||
\(412\) | −16.6676 | −0.821156 | ||||||||
\(413\) | 18.3240 | 0.901663 | ||||||||
\(414\) | 3.51522 | 0.172764 | ||||||||
\(415\) | 19.8006 | 0.971972 | ||||||||
\(416\) | 1.40671 | 0.0689698 | ||||||||
\(417\) | −37.2761 | −1.82542 | ||||||||
\(418\) | −9.67952 | −0.473441 | ||||||||
\(419\) | −10.5239 | −0.514128 | −0.257064 | − | 0.966394i | \(-0.582755\pi\) | ||||
−0.257064 | + | 0.966394i | \(0.582755\pi\) | |||||||
\(420\) | −49.6610 | −2.42321 | ||||||||
\(421\) | 1.50742 | 0.0734674 | 0.0367337 | − | 0.999325i | \(-0.488305\pi\) | ||||
0.0367337 | + | 0.999325i | \(0.488305\pi\) | |||||||
\(422\) | −4.23734 | −0.206270 | ||||||||
\(423\) | 7.32440 | 0.356125 | ||||||||
\(424\) | −25.0738 | −1.21769 | ||||||||
\(425\) | 7.22687 | 0.350555 | ||||||||
\(426\) | 31.8262 | 1.54198 | ||||||||
\(427\) | 10.4564 | 0.506019 | ||||||||
\(428\) | 30.1379 | 1.45677 | ||||||||
\(429\) | −30.1924 | −1.45770 | ||||||||
\(430\) | 33.4781 | 1.61446 | ||||||||
\(431\) | 6.17775 | 0.297572 | 0.148786 | − | 0.988869i | \(-0.452463\pi\) | ||||
0.148786 | + | 0.988869i | \(0.452463\pi\) | |||||||
\(432\) | −15.0411 | −0.723666 | ||||||||
\(433\) | −5.58124 | −0.268217 | −0.134109 | − | 0.990967i | \(-0.542817\pi\) | ||||
−0.134109 | + | 0.990967i | \(0.542817\pi\) | |||||||
\(434\) | 77.4034 | 3.71548 | ||||||||
\(435\) | −32.7079 | −1.56822 | ||||||||
\(436\) | −19.7424 | −0.945489 | ||||||||
\(437\) | −1.91027 | −0.0913808 | ||||||||
\(438\) | 39.8317 | 1.90323 | ||||||||
\(439\) | 11.4853 | 0.548164 | 0.274082 | − | 0.961706i | \(-0.411626\pi\) | ||||
0.274082 | + | 0.961706i | \(0.411626\pi\) | |||||||
\(440\) | 21.3879 | 1.01963 | ||||||||
\(441\) | 5.09702 | 0.242715 | ||||||||
\(442\) | −61.4850 | −2.92454 | ||||||||
\(443\) | 6.23410 | 0.296191 | 0.148096 | − | 0.988973i | \(-0.452686\pi\) | ||||
0.148096 | + | 0.988973i | \(0.452686\pi\) | |||||||
\(444\) | −0.593298 | −0.0281567 | ||||||||
\(445\) | 14.3546 | 0.680472 | ||||||||
\(446\) | 27.6804 | 1.31071 | ||||||||
\(447\) | 10.8931 | 0.515224 | ||||||||
\(448\) | −25.7423 | −1.21621 | ||||||||
\(449\) | −19.2240 | −0.907236 | −0.453618 | − | 0.891196i | \(-0.649867\pi\) | ||||
−0.453618 | + | 0.891196i | \(0.649867\pi\) | |||||||
\(450\) | 5.35318 | 0.252351 | ||||||||
\(451\) | 16.4060 | 0.772529 | ||||||||
\(452\) | 60.0354 | 2.82383 | ||||||||
\(453\) | −43.4043 | −2.03931 | ||||||||
\(454\) | 42.0237 | 1.97227 | ||||||||
\(455\) | 36.7404 | 1.72242 | ||||||||
\(456\) | −16.8236 | −0.787835 | ||||||||
\(457\) | −25.1834 | −1.17803 | −0.589016 | − | 0.808121i | \(-0.700485\pi\) | ||||
−0.589016 | + | 0.808121i | \(0.700485\pi\) | |||||||
\(458\) | 17.2304 | 0.805125 | ||||||||
\(459\) | 14.8598 | 0.693598 | ||||||||
\(460\) | 8.39336 | 0.391342 | ||||||||
\(461\) | −29.5473 | −1.37616 | −0.688078 | − | 0.725636i | \(-0.741545\pi\) | ||||
−0.688078 | + | 0.725636i | \(0.741545\pi\) | |||||||
\(462\) | −40.3580 | −1.87763 | ||||||||
\(463\) | 24.9805 | 1.16094 | 0.580471 | − | 0.814281i | \(-0.302868\pi\) | ||||
0.580471 | + | 0.814281i | \(0.302868\pi\) | |||||||
\(464\) | 36.5974 | 1.69899 | ||||||||
\(465\) | 34.9810 | 1.62221 | ||||||||
\(466\) | −61.9366 | −2.86916 | ||||||||
\(467\) | 18.8022 | 0.870061 | 0.435030 | − | 0.900416i | \(-0.356738\pi\) | ||||
0.435030 | + | 0.900416i | \(0.356738\pi\) | |||||||
\(468\) | −30.4212 | −1.40622 | ||||||||
\(469\) | 8.82494 | 0.407498 | ||||||||
\(470\) | 26.1824 | 1.20770 | ||||||||
\(471\) | 11.5432 | 0.531882 | ||||||||
\(472\) | −27.2749 | −1.25543 | ||||||||
\(473\) | 18.1728 | 0.835588 | ||||||||
\(474\) | 61.2767 | 2.81453 | ||||||||
\(475\) | −2.90907 | −0.133477 | ||||||||
\(476\) | −54.8969 | −2.51619 | ||||||||
\(477\) | 6.23366 | 0.285419 | ||||||||
\(478\) | −39.7146 | −1.81651 | ||||||||
\(479\) | −2.90297 | −0.132640 | −0.0663201 | − | 0.997798i | \(-0.521126\pi\) | ||||
−0.0663201 | + | 0.997798i | \(0.521126\pi\) | |||||||
\(480\) | 0.849787 | 0.0387873 | ||||||||
\(481\) | 0.438937 | 0.0200138 | ||||||||
\(482\) | 50.2663 | 2.28957 | ||||||||
\(483\) | −7.96474 | −0.362408 | ||||||||
\(484\) | −21.1695 | −0.962250 | ||||||||
\(485\) | 30.9733 | 1.40643 | ||||||||
\(486\) | 29.7109 | 1.34771 | ||||||||
\(487\) | 13.1114 | 0.594132 | 0.297066 | − | 0.954857i | \(-0.403992\pi\) | ||||
0.297066 | + | 0.954857i | \(0.403992\pi\) | |||||||
\(488\) | −15.5641 | −0.704553 | ||||||||
\(489\) | 30.0141 | 1.35728 | ||||||||
\(490\) | 18.2202 | 0.823104 | ||||||||
\(491\) | 23.7244 | 1.07067 | 0.535333 | − | 0.844641i | \(-0.320186\pi\) | ||||
0.535333 | + | 0.844641i | \(0.320186\pi\) | |||||||
\(492\) | 56.7014 | 2.55629 | ||||||||
\(493\) | −36.1564 | −1.62840 | ||||||||
\(494\) | 24.7499 | 1.11355 | ||||||||
\(495\) | −5.31730 | −0.238995 | ||||||||
\(496\) | −39.1409 | −1.75748 | ||||||||
\(497\) | −21.0229 | −0.943004 | ||||||||
\(498\) | 55.6139 | 2.49212 | ||||||||
\(499\) | 13.0002 | 0.581967 | 0.290983 | − | 0.956728i | \(-0.406018\pi\) | ||||
0.290983 | + | 0.956728i | \(0.406018\pi\) | |||||||
\(500\) | 48.9528 | 2.18924 | ||||||||
\(501\) | −45.4357 | −2.02992 | ||||||||
\(502\) | 53.2844 | 2.37820 | ||||||||
\(503\) | 20.1820 | 0.899871 | 0.449936 | − | 0.893061i | \(-0.351447\pi\) | ||||
0.449936 | + | 0.893061i | \(0.351447\pi\) | |||||||
\(504\) | −20.4495 | −0.910893 | ||||||||
\(505\) | −11.3938 | −0.507016 | ||||||||
\(506\) | 6.82104 | 0.303232 | ||||||||
\(507\) | 50.4488 | 2.24051 | ||||||||
\(508\) | 54.9210 | 2.43672 | ||||||||
\(509\) | 22.0919 | 0.979205 | 0.489603 | − | 0.871946i | \(-0.337142\pi\) | ||||
0.489603 | + | 0.871946i | \(0.337142\pi\) | |||||||
\(510\) | −37.1427 | −1.64471 | ||||||||
\(511\) | −26.3109 | −1.16393 | ||||||||
\(512\) | 40.1649 | 1.77505 | ||||||||
\(513\) | −5.98161 | −0.264095 | ||||||||
\(514\) | 74.9201 | 3.30458 | ||||||||
\(515\) | 7.44917 | 0.328249 | ||||||||
\(516\) | 62.8077 | 2.76496 | ||||||||
\(517\) | 14.2125 | 0.625065 | ||||||||
\(518\) | 0.586724 | 0.0257792 | ||||||||
\(519\) | −43.7951 | −1.92239 | ||||||||
\(520\) | −54.6874 | −2.39820 | ||||||||
\(521\) | 33.0366 | 1.44736 | 0.723680 | − | 0.690136i | \(-0.242449\pi\) | ||||
0.723680 | + | 0.690136i | \(0.242449\pi\) | |||||||
\(522\) | −26.7822 | −1.17223 | ||||||||
\(523\) | 0.267661 | 0.0117040 | 0.00585200 | − | 0.999983i | \(-0.498137\pi\) | ||||
0.00585200 | + | 0.999983i | \(0.498137\pi\) | |||||||
\(524\) | −54.9873 | −2.40213 | ||||||||
\(525\) | −12.1292 | −0.529360 | ||||||||
\(526\) | −30.0432 | −1.30995 | ||||||||
\(527\) | 38.6692 | 1.68446 | ||||||||
\(528\) | 20.4080 | 0.888144 | ||||||||
\(529\) | −21.6539 | −0.941472 | ||||||||
\(530\) | 22.2833 | 0.967924 | ||||||||
\(531\) | 6.78087 | 0.294265 | ||||||||
\(532\) | 22.0979 | 0.958067 | ||||||||
\(533\) | −41.9491 | −1.81702 | ||||||||
\(534\) | 40.3177 | 1.74472 | ||||||||
\(535\) | −13.4694 | −0.582331 | ||||||||
\(536\) | −13.1357 | −0.567378 | ||||||||
\(537\) | −45.0273 | −1.94307 | ||||||||
\(538\) | 12.7189 | 0.548352 | ||||||||
\(539\) | 9.89041 | 0.426010 | ||||||||
\(540\) | 26.2820 | 1.13100 | ||||||||
\(541\) | −2.23202 | −0.0959619 | −0.0479809 | − | 0.998848i | \(-0.515279\pi\) | ||||
−0.0479809 | + | 0.998848i | \(0.515279\pi\) | |||||||
\(542\) | −18.1638 | −0.780202 | ||||||||
\(543\) | −2.10982 | −0.0905409 | ||||||||
\(544\) | 0.939383 | 0.0402757 | ||||||||
\(545\) | 8.82334 | 0.377950 | ||||||||
\(546\) | 103.193 | 4.41625 | ||||||||
\(547\) | −35.3960 | −1.51342 | −0.756711 | − | 0.653750i | \(-0.773195\pi\) | ||||
−0.756711 | + | 0.653750i | \(0.773195\pi\) | |||||||
\(548\) | −40.2179 | −1.71802 | ||||||||
\(549\) | 3.86943 | 0.165143 | ||||||||
\(550\) | 10.3875 | 0.442923 | ||||||||
\(551\) | 14.5542 | 0.620031 | ||||||||
\(552\) | 11.8554 | 0.504597 | ||||||||
\(553\) | −40.4765 | −1.72124 | ||||||||
\(554\) | −22.6440 | −0.962051 | ||||||||
\(555\) | 0.265159 | 0.0112554 | ||||||||
\(556\) | −72.8799 | −3.09080 | ||||||||
\(557\) | −11.4950 | −0.487057 | −0.243528 | − | 0.969894i | \(-0.578305\pi\) | ||||
−0.243528 | + | 0.969894i | \(0.578305\pi\) | |||||||
\(558\) | 28.6435 | 1.21258 | ||||||||
\(559\) | −46.4667 | −1.96533 | ||||||||
\(560\) | −24.8340 | −1.04943 | ||||||||
\(561\) | −20.1621 | −0.851243 | ||||||||
\(562\) | 32.6097 | 1.37556 | ||||||||
\(563\) | −16.2612 | −0.685328 | −0.342664 | − | 0.939458i | \(-0.611329\pi\) | ||||
−0.342664 | + | 0.939458i | \(0.611329\pi\) | |||||||
\(564\) | 49.1203 | 2.06834 | ||||||||
\(565\) | −26.8312 | −1.12880 | ||||||||
\(566\) | −53.6119 | −2.25348 | ||||||||
\(567\) | −37.2947 | −1.56623 | ||||||||
\(568\) | 31.2921 | 1.31299 | ||||||||
\(569\) | −20.8098 | −0.872392 | −0.436196 | − | 0.899852i | \(-0.643675\pi\) | ||||
−0.436196 | + | 0.899852i | \(0.643675\pi\) | |||||||
\(570\) | 14.9513 | 0.626239 | ||||||||
\(571\) | 34.6094 | 1.44836 | 0.724180 | − | 0.689612i | \(-0.242219\pi\) | ||||
0.724180 | + | 0.689612i | \(0.242219\pi\) | |||||||
\(572\) | −59.0303 | −2.46818 | ||||||||
\(573\) | −40.0790 | −1.67432 | ||||||||
\(574\) | −56.0731 | −2.34045 | ||||||||
\(575\) | 2.04999 | 0.0854904 | ||||||||
\(576\) | −9.52606 | −0.396919 | ||||||||
\(577\) | 38.2923 | 1.59413 | 0.797066 | − | 0.603893i | \(-0.206384\pi\) | ||||
0.797066 | + | 0.603893i | \(0.206384\pi\) | |||||||
\(578\) | 0.663184 | 0.0275848 | ||||||||
\(579\) | 17.1429 | 0.712436 | ||||||||
\(580\) | −63.9484 | −2.65531 | ||||||||
\(581\) | −36.7359 | −1.52406 | ||||||||
\(582\) | 86.9947 | 3.60605 | ||||||||
\(583\) | 12.0960 | 0.500964 | ||||||||
\(584\) | 39.1633 | 1.62059 | ||||||||
\(585\) | 13.5960 | 0.562124 | ||||||||
\(586\) | −31.0326 | −1.28194 | ||||||||
\(587\) | −21.9669 | −0.906671 | −0.453335 | − | 0.891340i | \(-0.649766\pi\) | ||||
−0.453335 | + | 0.891340i | \(0.649766\pi\) | |||||||
\(588\) | 34.1826 | 1.40967 | ||||||||
\(589\) | −15.5657 | −0.641374 | ||||||||
\(590\) | 24.2394 | 0.997921 | ||||||||
\(591\) | 22.1851 | 0.912574 | ||||||||
\(592\) | −0.296691 | −0.0121939 | ||||||||
\(593\) | −37.3898 | −1.53541 | −0.767707 | − | 0.640802i | \(-0.778602\pi\) | ||||
−0.767707 | + | 0.640802i | \(0.778602\pi\) | |||||||
\(594\) | 21.3586 | 0.876356 | ||||||||
\(595\) | 24.5347 | 1.00583 | ||||||||
\(596\) | 21.2974 | 0.872376 | ||||||||
\(597\) | −20.6114 | −0.843569 | ||||||||
\(598\) | −17.4410 | −0.713214 | ||||||||
\(599\) | −14.3567 | −0.586599 | −0.293299 | − | 0.956021i | \(-0.594753\pi\) | ||||
−0.293299 | + | 0.956021i | \(0.594753\pi\) | |||||||
\(600\) | 18.0540 | 0.737052 | ||||||||
\(601\) | −45.1903 | −1.84335 | −0.921675 | − | 0.387962i | \(-0.873179\pi\) | ||||
−0.921675 | + | 0.387962i | \(0.873179\pi\) | |||||||
\(602\) | −62.1118 | −2.53149 | ||||||||
\(603\) | 3.26571 | 0.132990 | ||||||||
\(604\) | −84.8613 | −3.45296 | ||||||||
\(605\) | 9.46115 | 0.384650 | ||||||||
\(606\) | −32.0017 | −1.29998 | ||||||||
\(607\) | 22.8345 | 0.926823 | 0.463412 | − | 0.886143i | \(-0.346625\pi\) | ||||
0.463412 | + | 0.886143i | \(0.346625\pi\) | |||||||
\(608\) | −0.378135 | −0.0153354 | ||||||||
\(609\) | 60.6828 | 2.45899 | ||||||||
\(610\) | 13.8320 | 0.560039 | ||||||||
\(611\) | −36.3404 | −1.47018 | ||||||||
\(612\) | −20.3149 | −0.821180 | ||||||||
\(613\) | 14.4611 | 0.584079 | 0.292040 | − | 0.956406i | \(-0.405666\pi\) | ||||
0.292040 | + | 0.956406i | \(0.405666\pi\) | |||||||
\(614\) | 39.5694 | 1.59689 | ||||||||
\(615\) | −25.3412 | −1.02186 | ||||||||
\(616\) | −39.6808 | −1.59879 | ||||||||
\(617\) | −21.3647 | −0.860109 | −0.430055 | − | 0.902803i | \(-0.641506\pi\) | ||||
−0.430055 | + | 0.902803i | \(0.641506\pi\) | |||||||
\(618\) | 20.9225 | 0.841625 | ||||||||
\(619\) | −10.4054 | −0.418230 | −0.209115 | − | 0.977891i | \(-0.567058\pi\) | ||||
−0.209115 | + | 0.977891i | \(0.567058\pi\) | |||||||
\(620\) | 68.3926 | 2.74671 | ||||||||
\(621\) | 4.21517 | 0.169149 | ||||||||
\(622\) | 24.6619 | 0.988852 | ||||||||
\(623\) | −26.6320 | −1.06699 | ||||||||
\(624\) | −52.1819 | −2.08895 | ||||||||
\(625\) | −13.0438 | −0.521752 | ||||||||
\(626\) | 66.2893 | 2.64945 | ||||||||
\(627\) | 8.11594 | 0.324120 | ||||||||
\(628\) | 22.5685 | 0.900582 | ||||||||
\(629\) | 0.293116 | 0.0116873 | ||||||||
\(630\) | 18.1737 | 0.724056 | ||||||||
\(631\) | 22.0522 | 0.877885 | 0.438942 | − | 0.898515i | \(-0.355353\pi\) | ||||
0.438942 | + | 0.898515i | \(0.355353\pi\) | |||||||
\(632\) | 60.2485 | 2.39656 | ||||||||
\(633\) | 3.55286 | 0.141214 | ||||||||
\(634\) | 10.9814 | 0.436129 | ||||||||
\(635\) | −24.5455 | −0.974058 | ||||||||
\(636\) | 41.8053 | 1.65769 | ||||||||
\(637\) | −25.2891 | −1.00199 | ||||||||
\(638\) | −51.9690 | −2.05747 | ||||||||
\(639\) | −7.77961 | −0.307757 | ||||||||
\(640\) | −34.8785 | −1.37869 | ||||||||
\(641\) | 16.5002 | 0.651718 | 0.325859 | − | 0.945418i | \(-0.394347\pi\) | ||||
0.325859 | + | 0.945418i | \(0.394347\pi\) | |||||||
\(642\) | −37.8314 | −1.49309 | ||||||||
\(643\) | 2.83706 | 0.111883 | 0.0559414 | − | 0.998434i | \(-0.482184\pi\) | ||||
0.0559414 | + | 0.998434i | \(0.482184\pi\) | |||||||
\(644\) | −15.5722 | −0.613629 | ||||||||
\(645\) | −28.0703 | −1.10527 | ||||||||
\(646\) | 16.5276 | 0.650270 | ||||||||
\(647\) | −9.84659 | −0.387109 | −0.193555 | − | 0.981089i | \(-0.562002\pi\) | ||||
−0.193555 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(648\) | 55.5124 | 2.18073 | ||||||||
\(649\) | 13.1578 | 0.516489 | ||||||||
\(650\) | −26.5601 | −1.04177 | ||||||||
\(651\) | −64.9001 | −2.54364 | ||||||||
\(652\) | 58.6816 | 2.29815 | ||||||||
\(653\) | −46.5592 | −1.82200 | −0.911002 | − | 0.412402i | \(-0.864690\pi\) | ||||
−0.911002 | + | 0.412402i | \(0.864690\pi\) | |||||||
\(654\) | 24.7821 | 0.969058 | ||||||||
\(655\) | 24.5751 | 0.960230 | ||||||||
\(656\) | 28.3547 | 1.10707 | ||||||||
\(657\) | −9.73649 | −0.379857 | ||||||||
\(658\) | −48.5760 | −1.89369 | ||||||||
\(659\) | −10.5390 | −0.410539 | −0.205270 | − | 0.978705i | \(-0.565807\pi\) | ||||
−0.205270 | + | 0.978705i | \(0.565807\pi\) | |||||||
\(660\) | −35.6598 | −1.38806 | ||||||||
\(661\) | −21.1487 | −0.822589 | −0.411294 | − | 0.911503i | \(-0.634923\pi\) | ||||
−0.411294 | + | 0.911503i | \(0.634923\pi\) | |||||||
\(662\) | −17.9004 | −0.695720 | ||||||||
\(663\) | 51.5530 | 2.00215 | ||||||||
\(664\) | 54.6807 | 2.12202 | ||||||||
\(665\) | −9.87609 | −0.382978 | ||||||||
\(666\) | 0.217120 | 0.00841324 | ||||||||
\(667\) | −10.2562 | −0.397121 | ||||||||
\(668\) | −88.8330 | −3.43705 | ||||||||
\(669\) | −23.2091 | −0.897315 | ||||||||
\(670\) | 11.6739 | 0.451001 | ||||||||
\(671\) | 7.50836 | 0.289857 | ||||||||
\(672\) | −1.57661 | −0.0608189 | ||||||||
\(673\) | −46.8511 | −1.80598 | −0.902989 | − | 0.429664i | \(-0.858632\pi\) | ||||
−0.902989 | + | 0.429664i | \(0.858632\pi\) | |||||||
\(674\) | −27.8319 | −1.07205 | ||||||||
\(675\) | 6.41910 | 0.247071 | ||||||||
\(676\) | 98.6342 | 3.79362 | ||||||||
\(677\) | −0.579010 | −0.0222532 | −0.0111266 | − | 0.999938i | \(-0.503542\pi\) | ||||
−0.0111266 | + | 0.999938i | \(0.503542\pi\) | |||||||
\(678\) | −75.3609 | −2.89422 | ||||||||
\(679\) | −57.4646 | −2.20529 | ||||||||
\(680\) | −36.5194 | −1.40046 | ||||||||
\(681\) | −35.2354 | −1.35022 | ||||||||
\(682\) | 55.5808 | 2.12830 | ||||||||
\(683\) | 41.3272 | 1.58134 | 0.790671 | − | 0.612241i | \(-0.209732\pi\) | ||||
0.790671 | + | 0.612241i | \(0.209732\pi\) | |||||||
\(684\) | 8.17745 | 0.312673 | ||||||||
\(685\) | 17.9743 | 0.686763 | ||||||||
\(686\) | 23.5072 | 0.897510 | ||||||||
\(687\) | −14.4471 | −0.551192 | ||||||||
\(688\) | 31.4083 | 1.19743 | ||||||||
\(689\) | −30.9286 | −1.17829 | ||||||||
\(690\) | −10.5360 | −0.401097 | ||||||||
\(691\) | 35.2881 | 1.34242 | 0.671210 | − | 0.741267i | \(-0.265775\pi\) | ||||
0.671210 | + | 0.741267i | \(0.265775\pi\) | |||||||
\(692\) | −85.6254 | −3.25499 | ||||||||
\(693\) | 9.86516 | 0.374746 | ||||||||
\(694\) | 10.4504 | 0.396691 | ||||||||
\(695\) | 32.5718 | 1.23552 | ||||||||
\(696\) | −90.3251 | −3.42376 | ||||||||
\(697\) | −28.0130 | −1.06107 | ||||||||
\(698\) | 34.9446 | 1.32267 | ||||||||
\(699\) | 51.9317 | 1.96424 | ||||||||
\(700\) | −23.7142 | −0.896311 | ||||||||
\(701\) | −11.9185 | −0.450157 | −0.225079 | − | 0.974341i | \(-0.572264\pi\) | ||||
−0.225079 | + | 0.974341i | \(0.572264\pi\) | |||||||
\(702\) | −54.6126 | −2.06122 | ||||||||
\(703\) | −0.117989 | −0.00445005 | ||||||||
\(704\) | −18.4847 | −0.696667 | ||||||||
\(705\) | −21.9530 | −0.826798 | ||||||||
\(706\) | −78.8297 | −2.96680 | ||||||||
\(707\) | 21.1388 | 0.795006 | ||||||||
\(708\) | 45.4751 | 1.70906 | ||||||||
\(709\) | −24.6289 | −0.924959 | −0.462480 | − | 0.886630i | \(-0.653040\pi\) | ||||
−0.462480 | + | 0.886630i | \(0.653040\pi\) | |||||||
\(710\) | −27.8096 | −1.04368 | ||||||||
\(711\) | −14.9785 | −0.561739 | ||||||||
\(712\) | 39.6412 | 1.48562 | ||||||||
\(713\) | 10.9690 | 0.410791 | ||||||||
\(714\) | 68.9107 | 2.57892 | ||||||||
\(715\) | 26.3820 | 0.986632 | ||||||||
\(716\) | −88.0345 | −3.29000 | ||||||||
\(717\) | 33.2994 | 1.24359 | ||||||||
\(718\) | 23.5035 | 0.877141 | ||||||||
\(719\) | 28.1922 | 1.05139 | 0.525695 | − | 0.850673i | \(-0.323805\pi\) | ||||
0.525695 | + | 0.850673i | \(0.323805\pi\) | |||||||
\(720\) | −9.18994 | −0.342489 | ||||||||
\(721\) | −13.8204 | −0.514699 | ||||||||
\(722\) | 39.9775 | 1.48781 | ||||||||
\(723\) | −42.1466 | −1.56745 | ||||||||
\(724\) | −4.12498 | −0.153304 | ||||||||
\(725\) | −15.6187 | −0.580064 | ||||||||
\(726\) | 26.5735 | 0.986236 | ||||||||
\(727\) | −36.5849 | −1.35686 | −0.678429 | − | 0.734666i | \(-0.737339\pi\) | ||||
−0.678429 | + | 0.734666i | \(0.737339\pi\) | |||||||
\(728\) | 101.461 | 3.76040 | ||||||||
\(729\) | 8.62695 | 0.319517 | ||||||||
\(730\) | −34.8048 | −1.28818 | ||||||||
\(731\) | −31.0298 | −1.14768 | ||||||||
\(732\) | 25.9499 | 0.959135 | ||||||||
\(733\) | −39.2120 | −1.44833 | −0.724164 | − | 0.689628i | \(-0.757774\pi\) | ||||
−0.724164 | + | 0.689628i | \(0.757774\pi\) | |||||||
\(734\) | −5.36673 | −0.198090 | ||||||||
\(735\) | −15.2770 | −0.563501 | ||||||||
\(736\) | 0.266467 | 0.00982211 | ||||||||
\(737\) | 6.33689 | 0.233422 | ||||||||
\(738\) | −20.7501 | −0.763823 | ||||||||
\(739\) | 46.6007 | 1.71424 | 0.857118 | − | 0.515121i | \(-0.172253\pi\) | ||||
0.857118 | + | 0.515121i | \(0.172253\pi\) | |||||||
\(740\) | 0.518422 | 0.0190576 | ||||||||
\(741\) | −20.7519 | −0.762341 | ||||||||
\(742\) | −41.3421 | −1.51772 | ||||||||
\(743\) | −18.6904 | −0.685683 | −0.342841 | − | 0.939393i | \(-0.611389\pi\) | ||||
−0.342841 | + | 0.939393i | \(0.611389\pi\) | |||||||
\(744\) | 96.6025 | 3.54162 | ||||||||
\(745\) | −9.51832 | −0.348724 | ||||||||
\(746\) | −32.3565 | −1.18466 | ||||||||
\(747\) | −13.5943 | −0.497390 | ||||||||
\(748\) | −39.4196 | −1.44132 | ||||||||
\(749\) | 24.9896 | 0.913102 | ||||||||
\(750\) | −61.4492 | −2.24381 | ||||||||
\(751\) | 33.6658 | 1.22848 | 0.614241 | − | 0.789118i | \(-0.289462\pi\) | ||||
0.614241 | + | 0.789118i | \(0.289462\pi\) | |||||||
\(752\) | 24.5636 | 0.895743 | ||||||||
\(753\) | −44.6771 | −1.62812 | ||||||||
\(754\) | 132.881 | 4.83925 | ||||||||
\(755\) | 37.9265 | 1.38029 | ||||||||
\(756\) | −48.7609 | −1.77342 | ||||||||
\(757\) | 16.0511 | 0.583389 | 0.291694 | − | 0.956512i | \(-0.405781\pi\) | ||||
0.291694 | + | 0.956512i | \(0.405781\pi\) | |||||||
\(758\) | 6.85696 | 0.249056 | ||||||||
\(759\) | −5.71921 | −0.207594 | ||||||||
\(760\) | 14.7004 | 0.533238 | ||||||||
\(761\) | 7.56687 | 0.274299 | 0.137149 | − | 0.990550i | \(-0.456206\pi\) | ||||
0.137149 | + | 0.990550i | \(0.456206\pi\) | |||||||
\(762\) | −68.9409 | −2.49747 | ||||||||
\(763\) | −16.3699 | −0.592630 | ||||||||
\(764\) | −78.3599 | −2.83496 | ||||||||
\(765\) | 9.07919 | 0.328259 | ||||||||
\(766\) | 37.6006 | 1.35857 | ||||||||
\(767\) | −33.6437 | −1.21480 | ||||||||
\(768\) | −66.2052 | −2.38897 | ||||||||
\(769\) | −4.77046 | −0.172027 | −0.0860135 | − | 0.996294i | \(-0.527413\pi\) | ||||
−0.0860135 | + | 0.996294i | \(0.527413\pi\) | |||||||
\(770\) | 35.2647 | 1.27085 | ||||||||
\(771\) | −62.8179 | −2.26233 | ||||||||
\(772\) | 33.5168 | 1.20629 | ||||||||
\(773\) | 51.2454 | 1.84317 | 0.921585 | − | 0.388177i | \(-0.126895\pi\) | ||||
0.921585 | + | 0.388177i | \(0.126895\pi\) | |||||||
\(774\) | −22.9848 | −0.826171 | ||||||||
\(775\) | 16.7042 | 0.600032 | ||||||||
\(776\) | 85.5349 | 3.07052 | ||||||||
\(777\) | −0.491948 | −0.0176485 | ||||||||
\(778\) | −15.2290 | −0.545988 | ||||||||
\(779\) | 11.2762 | 0.404013 | ||||||||
\(780\) | 91.1798 | 3.26476 | ||||||||
\(781\) | −15.0958 | −0.540170 | ||||||||
\(782\) | −11.6468 | −0.416489 | ||||||||
\(783\) | −32.1151 | −1.14770 | ||||||||
\(784\) | 17.0937 | 0.610490 | ||||||||
\(785\) | −10.0864 | −0.359999 | ||||||||
\(786\) | 69.0242 | 2.46201 | ||||||||
\(787\) | −17.9526 | −0.639942 | −0.319971 | − | 0.947427i | \(-0.603673\pi\) | ||||
−0.319971 | + | 0.947427i | \(0.603673\pi\) | |||||||
\(788\) | 43.3749 | 1.54517 | ||||||||
\(789\) | 25.1902 | 0.896794 | ||||||||
\(790\) | −53.5434 | −1.90499 | ||||||||
\(791\) | 49.7799 | 1.76997 | ||||||||
\(792\) | −14.6841 | −0.521776 | ||||||||
\(793\) | −19.1984 | −0.681754 | ||||||||
\(794\) | −37.5654 | −1.33315 | ||||||||
\(795\) | −18.6838 | −0.662645 | ||||||||
\(796\) | −40.2981 | −1.42833 | ||||||||
\(797\) | 6.23298 | 0.220783 | 0.110392 | − | 0.993888i | \(-0.464789\pi\) | ||||
0.110392 | + | 0.993888i | \(0.464789\pi\) | |||||||
\(798\) | −27.7390 | −0.981949 | ||||||||
\(799\) | −24.2676 | −0.858526 | ||||||||
\(800\) | 0.405791 | 0.0143469 | ||||||||
\(801\) | −9.85529 | −0.348220 | ||||||||
\(802\) | −45.6625 | −1.61240 | ||||||||
\(803\) | −18.8930 | −0.666719 | ||||||||
\(804\) | 21.9011 | 0.772393 | ||||||||
\(805\) | 6.95957 | 0.245292 | ||||||||
\(806\) | −142.116 | −5.00583 | ||||||||
\(807\) | −10.6644 | −0.375404 | ||||||||
\(808\) | −31.4647 | −1.10692 | ||||||||
\(809\) | −21.5073 | −0.756156 | −0.378078 | − | 0.925774i | \(-0.623415\pi\) | ||||
−0.378078 | + | 0.925774i | \(0.623415\pi\) | |||||||
\(810\) | −49.3344 | −1.73343 | ||||||||
\(811\) | −35.2682 | −1.23843 | −0.619216 | − | 0.785220i | \(-0.712550\pi\) | ||||
−0.619216 | + | 0.785220i | \(0.712550\pi\) | |||||||
\(812\) | 118.643 | 4.16356 | ||||||||
\(813\) | 15.2297 | 0.534129 | ||||||||
\(814\) | 0.421307 | 0.0147668 | ||||||||
\(815\) | −26.2262 | −0.918664 | ||||||||
\(816\) | −34.8463 | −1.21987 | ||||||||
\(817\) | 12.4906 | 0.436991 | ||||||||
\(818\) | −69.5373 | −2.43131 | ||||||||
\(819\) | −25.2245 | −0.881417 | ||||||||
\(820\) | −49.5455 | −1.73020 | ||||||||
\(821\) | 32.2222 | 1.12456 | 0.562282 | − | 0.826946i | \(-0.309924\pi\) | ||||
0.562282 | + | 0.826946i | \(0.309924\pi\) | |||||||
\(822\) | 50.4845 | 1.76085 | ||||||||
\(823\) | 37.9085 | 1.32141 | 0.660704 | − | 0.750647i | \(-0.270258\pi\) | ||||
0.660704 | + | 0.750647i | \(0.270258\pi\) | |||||||
\(824\) | 20.5714 | 0.716638 | ||||||||
\(825\) | −8.70953 | −0.303227 | ||||||||
\(826\) | −44.9713 | −1.56475 | ||||||||
\(827\) | 14.4159 | 0.501290 | 0.250645 | − | 0.968079i | \(-0.419357\pi\) | ||||
0.250645 | + | 0.968079i | \(0.419357\pi\) | |||||||
\(828\) | −5.76255 | −0.200263 | ||||||||
\(829\) | 9.87242 | 0.342883 | 0.171442 | − | 0.985194i | \(-0.445157\pi\) | ||||
0.171442 | + | 0.985194i | \(0.445157\pi\) | |||||||
\(830\) | −48.5952 | −1.68677 | ||||||||
\(831\) | 18.9862 | 0.658624 | ||||||||
\(832\) | 47.2641 | 1.63859 | ||||||||
\(833\) | −16.8877 | −0.585124 | ||||||||
\(834\) | 91.4843 | 3.16784 | ||||||||
\(835\) | 39.7016 | 1.37393 | ||||||||
\(836\) | 15.8678 | 0.548799 | ||||||||
\(837\) | 34.3470 | 1.18721 | ||||||||
\(838\) | 25.8282 | 0.892220 | ||||||||
\(839\) | −1.78012 | −0.0614566 | −0.0307283 | − | 0.999528i | \(-0.509783\pi\) | ||||
−0.0307283 | + | 0.999528i | \(0.509783\pi\) | |||||||
\(840\) | 61.2921 | 2.11478 | ||||||||
\(841\) | 49.1412 | 1.69452 | ||||||||
\(842\) | −3.69957 | −0.127496 | ||||||||
\(843\) | −27.3421 | −0.941712 | ||||||||
\(844\) | 6.94633 | 0.239103 | ||||||||
\(845\) | −44.0820 | −1.51647 | ||||||||
\(846\) | −17.9758 | −0.618021 | ||||||||
\(847\) | −17.5532 | −0.603136 | ||||||||
\(848\) | 20.9056 | 0.717902 | ||||||||
\(849\) | 44.9517 | 1.54274 | ||||||||
\(850\) | −17.7364 | −0.608354 | ||||||||
\(851\) | 0.0831457 | 0.00285020 | ||||||||
\(852\) | −52.1731 | −1.78742 | ||||||||
\(853\) | −30.6223 | −1.04849 | −0.524244 | − | 0.851568i | \(-0.675652\pi\) | ||||
−0.524244 | + | 0.851568i | \(0.675652\pi\) | |||||||
\(854\) | −25.6624 | −0.878148 | ||||||||
\(855\) | −3.65470 | −0.124988 | ||||||||
\(856\) | −37.1966 | −1.27135 | ||||||||
\(857\) | −7.51221 | −0.256612 | −0.128306 | − | 0.991735i | \(-0.540954\pi\) | ||||
−0.128306 | + | 0.991735i | \(0.540954\pi\) | |||||||
\(858\) | 74.0992 | 2.52971 | ||||||||
\(859\) | −26.1130 | −0.890965 | −0.445482 | − | 0.895291i | \(-0.646968\pi\) | ||||
−0.445482 | + | 0.895291i | \(0.646968\pi\) | |||||||
\(860\) | −54.8812 | −1.87143 | ||||||||
\(861\) | 47.0154 | 1.60228 | ||||||||
\(862\) | −15.1616 | −0.516408 | ||||||||
\(863\) | −28.2339 | −0.961091 | −0.480546 | − | 0.876970i | \(-0.659561\pi\) | ||||
−0.480546 | + | 0.876970i | \(0.659561\pi\) | |||||||
\(864\) | 0.834385 | 0.0283864 | ||||||||
\(865\) | 38.2680 | 1.30115 | ||||||||
\(866\) | 13.6977 | 0.465465 | ||||||||
\(867\) | −0.556057 | −0.0188847 | ||||||||
\(868\) | −126.889 | −4.30688 | ||||||||
\(869\) | −29.0648 | −0.985956 | ||||||||
\(870\) | 80.2728 | 2.72150 | ||||||||
\(871\) | −16.2030 | −0.549018 | ||||||||
\(872\) | 24.3663 | 0.825146 | ||||||||
\(873\) | −21.2651 | −0.719713 | ||||||||
\(874\) | 4.68826 | 0.158583 | ||||||||
\(875\) | 40.5905 | 1.37221 | ||||||||
\(876\) | −65.2966 | −2.20617 | ||||||||
\(877\) | −13.4117 | −0.452879 | −0.226440 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226440 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(878\) | −28.1876 | −0.951287 | ||||||||
\(879\) | 26.0197 | 0.877624 | ||||||||
\(880\) | −17.8324 | −0.601132 | ||||||||
\(881\) | 13.3596 | 0.450095 | 0.225048 | − | 0.974348i | \(-0.427746\pi\) | ||||
0.225048 | + | 0.974348i | \(0.427746\pi\) | |||||||
\(882\) | −12.5093 | −0.421209 | ||||||||
\(883\) | −29.8463 | −1.00441 | −0.502204 | − | 0.864749i | \(-0.667477\pi\) | ||||
−0.502204 | + | 0.864749i | \(0.667477\pi\) | |||||||
\(884\) | 100.793 | 3.39004 | ||||||||
\(885\) | −20.3239 | −0.683181 | ||||||||
\(886\) | −15.2999 | −0.514011 | ||||||||
\(887\) | 52.8372 | 1.77410 | 0.887049 | − | 0.461675i | \(-0.152751\pi\) | ||||
0.887049 | + | 0.461675i | \(0.152751\pi\) | |||||||
\(888\) | 0.732255 | 0.0245729 | ||||||||
\(889\) | 45.5391 | 1.52733 | ||||||||
\(890\) | −35.2295 | −1.18089 | ||||||||
\(891\) | −26.7801 | −0.897166 | ||||||||
\(892\) | −45.3769 | −1.51933 | ||||||||
\(893\) | 9.76857 | 0.326893 | ||||||||
\(894\) | −26.7341 | −0.894122 | ||||||||
\(895\) | 39.3447 | 1.31515 | ||||||||
\(896\) | 64.7099 | 2.16181 | ||||||||
\(897\) | 14.6236 | 0.488269 | ||||||||
\(898\) | 47.1801 | 1.57442 | ||||||||
\(899\) | −83.5718 | −2.78728 | ||||||||
\(900\) | −8.77554 | −0.292518 | ||||||||
\(901\) | −20.6537 | −0.688073 | ||||||||
\(902\) | −40.2642 | −1.34065 | ||||||||
\(903\) | 52.0786 | 1.73307 | ||||||||
\(904\) | −74.0963 | −2.46441 | ||||||||
\(905\) | 1.84355 | 0.0612817 | ||||||||
\(906\) | 106.524 | 3.53903 | ||||||||
\(907\) | 10.2924 | 0.341755 | 0.170877 | − | 0.985292i | \(-0.445340\pi\) | ||||
0.170877 | + | 0.985292i | \(0.445340\pi\) | |||||||
\(908\) | −68.8901 | −2.28620 | ||||||||
\(909\) | 7.82252 | 0.259456 | ||||||||
\(910\) | −90.1696 | −2.98909 | ||||||||
\(911\) | −8.10401 | −0.268498 | −0.134249 | − | 0.990948i | \(-0.542862\pi\) | ||||
−0.134249 | + | 0.990948i | \(0.542862\pi\) | |||||||
\(912\) | 14.0269 | 0.464476 | ||||||||
\(913\) | −26.3788 | −0.873011 | ||||||||
\(914\) | 61.8060 | 2.04436 | ||||||||
\(915\) | −11.5976 | −0.383405 | ||||||||
\(916\) | −28.2461 | −0.933277 | ||||||||
\(917\) | −45.5941 | −1.50565 | ||||||||
\(918\) | −36.4695 | −1.20367 | ||||||||
\(919\) | −53.3408 | −1.75955 | −0.879776 | − | 0.475388i | \(-0.842308\pi\) | ||||
−0.879776 | + | 0.475388i | \(0.842308\pi\) | |||||||
\(920\) | −10.3592 | −0.341532 | ||||||||
\(921\) | −33.1776 | −1.09324 | ||||||||
\(922\) | 72.5161 | 2.38819 | ||||||||
\(923\) | 38.5990 | 1.27050 | ||||||||
\(924\) | 66.1595 | 2.17649 | ||||||||
\(925\) | 0.126619 | 0.00416321 | ||||||||
\(926\) | −61.3080 | −2.01471 | ||||||||
\(927\) | −5.11431 | −0.167976 | ||||||||
\(928\) | −2.03019 | −0.0666444 | ||||||||
\(929\) | −53.9902 | −1.77136 | −0.885680 | − | 0.464296i | \(-0.846308\pi\) | ||||
−0.885680 | + | 0.464296i | \(0.846308\pi\) | |||||||
\(930\) | −85.8515 | −2.81518 | ||||||||
\(931\) | 6.79790 | 0.222792 | ||||||||
\(932\) | 101.534 | 3.32584 | ||||||||
\(933\) | −20.6781 | −0.676972 | ||||||||
\(934\) | −46.1449 | −1.50991 | ||||||||
\(935\) | 17.6175 | 0.576155 | ||||||||
\(936\) | 37.5462 | 1.22724 | ||||||||
\(937\) | 22.6819 | 0.740984 | 0.370492 | − | 0.928836i | \(-0.379189\pi\) | ||||
0.370492 | + | 0.928836i | \(0.379189\pi\) | |||||||
\(938\) | −21.6585 | −0.707174 | ||||||||
\(939\) | −55.5813 | −1.81383 | ||||||||
\(940\) | −42.9211 | −1.39993 | ||||||||
\(941\) | 41.9097 | 1.36622 | 0.683108 | − | 0.730318i | \(-0.260628\pi\) | ||||
0.683108 | + | 0.730318i | \(0.260628\pi\) | |||||||
\(942\) | −28.3297 | −0.923031 | ||||||||
\(943\) | −7.94622 | −0.258765 | ||||||||
\(944\) | 22.7408 | 0.740150 | ||||||||
\(945\) | 21.7924 | 0.708907 | ||||||||
\(946\) | −44.6004 | −1.45008 | ||||||||
\(947\) | 29.6824 | 0.964548 | 0.482274 | − | 0.876020i | \(-0.339811\pi\) | ||||
0.482274 | + | 0.876020i | \(0.339811\pi\) | |||||||
\(948\) | −100.452 | −3.26252 | ||||||||
\(949\) | 48.3081 | 1.56815 | ||||||||
\(950\) | 7.13954 | 0.231637 | ||||||||
\(951\) | −9.20756 | −0.298576 | ||||||||
\(952\) | 67.7543 | 2.19593 | ||||||||
\(953\) | −45.4176 | −1.47122 | −0.735610 | − | 0.677405i | \(-0.763104\pi\) | ||||
−0.735610 | + | 0.677405i | \(0.763104\pi\) | |||||||
\(954\) | −15.2988 | −0.495318 | ||||||||
\(955\) | 35.0209 | 1.13325 | ||||||||
\(956\) | 65.1048 | 2.10564 | ||||||||
\(957\) | 43.5742 | 1.40856 | ||||||||
\(958\) | 7.12457 | 0.230184 | ||||||||
\(959\) | −33.3477 | −1.07685 | ||||||||
\(960\) | 28.5519 | 0.921509 | ||||||||
\(961\) | 58.3799 | 1.88322 | ||||||||
\(962\) | −1.07725 | −0.0347320 | ||||||||
\(963\) | 9.24754 | 0.297998 | ||||||||
\(964\) | −82.4023 | −2.65400 | ||||||||
\(965\) | −14.9794 | −0.482205 | ||||||||
\(966\) | 19.5473 | 0.628925 | ||||||||
\(967\) | 51.5719 | 1.65844 | 0.829220 | − | 0.558923i | \(-0.188785\pi\) | ||||
0.829220 | + | 0.558923i | \(0.188785\pi\) | |||||||
\(968\) | 26.1276 | 0.839773 | ||||||||
\(969\) | −13.8578 | −0.445178 | ||||||||
\(970\) | −76.0157 | −2.44072 | ||||||||
\(971\) | −55.9459 | −1.79539 | −0.897695 | − | 0.440618i | \(-0.854759\pi\) | ||||
−0.897695 | + | 0.440618i | \(0.854759\pi\) | |||||||
\(972\) | −48.7055 | −1.56223 | ||||||||
\(973\) | −60.4302 | −1.93730 | ||||||||
\(974\) | −32.1783 | −1.03106 | ||||||||
\(975\) | 22.2697 | 0.713201 | ||||||||
\(976\) | 12.9768 | 0.415377 | ||||||||
\(977\) | 59.7613 | 1.91193 | 0.955966 | − | 0.293477i | \(-0.0948126\pi\) | ||||
0.955966 | + | 0.293477i | \(0.0948126\pi\) | |||||||
\(978\) | −73.6615 | −2.35544 | ||||||||
\(979\) | −19.1235 | −0.611190 | ||||||||
\(980\) | −29.8686 | −0.954118 | ||||||||
\(981\) | −6.05776 | −0.193410 | ||||||||
\(982\) | −58.2252 | −1.85804 | ||||||||
\(983\) | −2.19978 | −0.0701621 | −0.0350811 | − | 0.999384i | \(-0.511169\pi\) | ||||
−0.0350811 | + | 0.999384i | \(0.511169\pi\) | |||||||
\(984\) | −69.9814 | −2.23093 | ||||||||
\(985\) | −19.3853 | −0.617666 | ||||||||
\(986\) | 88.7362 | 2.82594 | ||||||||
\(987\) | 40.7293 | 1.29643 | ||||||||
\(988\) | −40.5729 | −1.29079 | ||||||||
\(989\) | −8.80198 | −0.279887 | ||||||||
\(990\) | 13.0499 | 0.414753 | ||||||||
\(991\) | −37.7818 | −1.20018 | −0.600089 | − | 0.799933i | \(-0.704868\pi\) | ||||
−0.600089 | + | 0.799933i | \(0.704868\pi\) | |||||||
\(992\) | 2.17129 | 0.0689385 | ||||||||
\(993\) | 15.0089 | 0.476293 | ||||||||
\(994\) | 51.5950 | 1.63649 | ||||||||
\(995\) | 18.0102 | 0.570962 | ||||||||
\(996\) | −91.1687 | −2.88879 | ||||||||
\(997\) | −25.9810 | −0.822826 | −0.411413 | − | 0.911449i | \(-0.634965\pi\) | ||||
−0.411413 | + | 0.911449i | \(0.634965\pi\) | |||||||
\(998\) | −31.9054 | −1.00995 | ||||||||
\(999\) | 0.260353 | 0.00823721 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6029.2.a.a.1.18 | ✓ | 234 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6029.2.a.a.1.18 | ✓ | 234 | 1.1 | even | 1 | trivial |